As you have already flown the first segment(s), LH will recalculate the cost of the new routing and those costs will be dependent on the new fare and the fare rules of your existing ticket.
I would call LH and ask for a price. You may be surprised as fares are not calculated based on distance, but rather demand. If you are flexible about where you will stay in Europe, you might check several destinations (although bear in mind that a cheap ticket might be to an expensive location).